Theory of the spatial structure of nonlinear lasing modes

A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multimode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a linear wave equation and not in terms of resonances of the cold cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found to have nontrivial spatial structure even in the single-mode limit. In the multimode regime spatial hole-burning and mode competition is treated exactly. The formalism generalizes to complex, chaotic, and random laser media.